Projection optical system and image display apparatus

ABSTRACT

There is provided a projection optical system capable of projecting an image formed on an image forming unit on a projection plane, which has an extremely short projection distance and a small size.

CROSS-REFERENCE TO RELATED APPLICATIONS

This patent application is based on and claims priority pursuant to 35U.S.C. §119 to Japanese Patent Application No. 2013-105851, filed on May20, 2013, in the Japan Patent Office, the entire disclosure of which ishereby incorporated by reference herein.

BACKGROUND

1. Technical Field

The present invention relates to a projection optical system, and animage display apparatus provided with the projection optical system.

2. Description of the Related Art

The image display apparatuses, such as projectors, are usually providedwith a projection optical system that magnifies and projects an image ona projection plane such as a screen. Recently, a demand for a projectorof which projection distance is extremely short and which can greatlymagnify a display size of an image on a screen (can implement a largescreen display), that is, a front projection type projector with anultra-short projection distance has been increased. In addition, arequest for miniaturization of the projector has also been increased.

SUMMARY

Example embodiments of the present invention include a projectionoptical system including: in order from a reduction side to amagnification side, an image forming unit configured to form an imagethereon; a refraction optical system including a plurality of lenses, afirst reflecting surface and a second reflecting surface. When, anoptical axis shared by the largest number of lenses among optical axesof the plurality of the lenses of the refraction optical system isdefined by an optical axis of the projection optical system, when inarrangement where a distance between an intersection of amagnification-side surface of a lens which is arranged to be closest tothe magnification side of the refraction optical system and the opticalaxis and an intersection of the first reflecting surface and the opticalaxis has a minimum value, the distance between the intersections isdenoted by L, when a focal length of the refraction optical system isdenoted by f, when a direction parallel to the optical axis is definedby a Z axis direction, when an arrangement direction of the firstreflecting surface and the second reflecting surface is defined by a Yaxis direction, when a maximum value of a distance between the opticalaxis and an end portion of the image forming unit in the Y axisdirection is denoted by Ymax, when in a YZ plane which is a planeparallel to the Y axis direction and the Z axis direction, a maximumvalue D1 of a distance between an intersection of a light beam path fromthe image forming unit and the magnification-side surface of the lenswhich is arranged to be closest to the magnification side of therefraction optical system and the optical axis, when a sag amount ds1which is a sag amount of the magnification-side surface of the lenswhich is arranged to be closest to the magnification side of therefraction optical system at the D1 and of which positive direction isdefined by the direction from the reduction side in the Z axis towardthe magnification side, when a point H of which distance from theoptical axis has a maximum value among the intersections of the lightbeam and the first reflecting surface, when a point F of which distancefrom the optical axis has a minimum value among the intersections of thelight beam and the second reflecting surface, an angle θ1 between a lineconnecting the H and the F and the optical axis satisfies the condition1: 0<Ymax/f−1/tan θ1; and condition 2: −0.1<(L−D1−ds1)/(L+D1−ds1)−1/tanθ1.

The above-described projection optical system may be applicable to anydesired apparatus such as an image display apparatus.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

FIG. 1 is an optical layout diagram illustrating an image displayapparatus according to an embodiment of the present invention;

FIG. 2 is a plan view illustrating an image forming unit included in theimage display apparatus of FIG. 1 as seen from an optical axisdirection;

FIG. 3 is an optical layout diagram illustrating an example of aprojection optical system included in the image display apparatus ofFIG. 1;

FIG. 4 is an optical layout diagram illustrating an example of aprojection optical system included in the image display apparatus ofFIG. 1;

FIG. 5 is an optical layout diagram illustrating a moving locus of eachof lens units constituting the projection optical system of FIG. 3during focusing;

FIG. 6 is a diagram illustrating an example of an image on a screen in along distance projection period of the projection optical system of FIG.3;

FIG. 7A is a diagram illustrating distortion in the upper side of theimage exemplified in FIG. 6;

FIG. 7B is a diagram illustrating distortion in the left end of theimage exemplified in FIG. 6;

FIG. 7C is a diagram illustrating distortion in the lower end of theimage exemplified in FIG. 6;

FIG. 8 is a diagram illustrating an example of an image on a screen in areference distance projection period of the projection optical system ofFIG. 3;

FIG. 9A is a diagram illustrating distortion in the upper side of theimage exemplified in FIG. 8;

FIG. 9B is a diagram illustrating distortion in the left end of theimage exemplified in FIG. 8;

FIG. 9C is a diagram illustrating distortion in the lower end of theimage exemplified in FIG. 8;

FIG. 10 is a diagram illustrating an example of an image on a screen ina close range projection period of the projection optical system of FIG.3;

FIG. 11A is a diagram illustrating distortion in the upper side of theimage exemplified in FIG. 10;

FIG. 11B is a diagram illustrating distortion in the left end of theimage exemplified in FIG. 10;

FIG. 11C is a diagram illustrating distortion in the lower end of theimage exemplified in FIG. 10;

FIG. 12 is a spot diagram in the long distance projection period of theprojection optical system of FIG. 3;

FIG. 13 is a spot diagram in the reference distance projection period ofthe projection optical system of FIG. 3;

FIG. 14 is a spot diagram in the close range projection period of theprojection optical system of FIG. 3;

FIG. 15 is an optical layout diagram illustrating an image displayapparatus according to another embodiment of the present invention;

FIG. 16 is an optical layout diagram illustrating a moving locus of eachof lens units constituting a projection optical system of FIG. 15 duringfocusing;

FIG. 17 is a diagram illustrating an example of an image on a screen ina long distance projection period of the projection optical system ofFIG. 15;

FIG. 18A is a diagram illustrating distortion in the upper side of theimage exemplified in FIG. 17;

FIG. 18B is a diagram illustrating distortion in the left end of theimage exemplified in FIG. 17;

FIG. 18C is a diagram illustrating distortion in the lower end of theimage exemplified in FIG. 17;

FIG. 19 is a diagram illustrating an example of an image on a screen ina reference distance projection period of the projection optical systemof FIG. 15;

FIG. 20A is a diagram illustrating distortion in the upper side of theimage exemplified in FIG. 19;

FIG. 20B is a diagram illustrating distortion in the left end of theimage exemplified in FIG. 19;

FIG. 20C is a diagram illustrating distortion in the lower end of theimage exemplified in FIG. 19;

FIG. 21 is a diagram illustrating an example of an image on a screen ina close range projection period of the projection optical system of FIG.15;

FIG. 22A is a diagram illustrating distortion in the upper side of theimage exemplified in FIG. 21;

FIG. 22B is a diagram illustrating distortion in the left end of theimage exemplified in FIG. 21;

FIG. 22C is a diagram illustrating distortion in the lower end of theimage exemplified in FIG. 21;

FIG. 23 is a spot diagram in the long distance projection period of theprojection optical system of FIG. 15;

FIG. 24 is a spot diagram in the reference distance projection period ofthe projection optical system of FIG. 15;

FIG. 25 is a spot diagram in the close range projection period of theprojection optical system of FIG. 15;

FIG. 26 is an optical layout diagram illustrating an image displayapparatus according to still another embodiment of the presentinvention;

FIG. 27 is an optical layout diagram illustrating a moving locus of eachof lens units constituting the projection optical system of FIG. 26during focusing;

FIG. 28 is a diagram illustrating an example of an image on a screen ina long distance projection period of the projection optical system ofFIG. 26;

FIG. 29A is a diagram illustrating distortion in the upper side of theimage exemplified in FIG. 28;

FIG. 29B is a diagram illustrating distortion in the left end of theimage exemplified in FIG. 28;

FIG. 29C is a diagram illustrating distortion in the lower end of theimage exemplified in FIG. 28;

FIG. 30 is a diagram illustrating an example of an image on a screen ina reference distance projection period of the projection optical systemof FIG. 26;

FIG. 31A is a diagram illustrating distortion in the upper side of theimage exemplified in FIG. 30;

FIG. 31B is a diagram illustrating distortion in the left end of theimage exemplified in FIG. 30;

FIG. 31C is a diagram illustrating distortion in the lower end of theimage exemplified in FIG. 30;

FIG. 32 is a diagram illustrating an example of an image on a screen ina close range projection period of the projection optical system of FIG.26;

FIG. 33A is a diagram illustrating distortion in the upper side of theimage exemplified in FIG. 32;

FIG. 33B is a diagram illustrating distortion in the left end of theimage exemplified in FIG. 32;

FIG. 33C is a diagram illustrating distortion in the lower end of theimage exemplified in FIG. 32;

FIG. 34 is a spot diagram in the long distance projection period of theprojection optical system of FIG. 26;

FIG. 35 is a spot diagram in the reference distance projection period ofthe projection optical system of FIG. 26;

FIG. 36 is a spot diagram in the close range projection period of theprojection optical system of FIG. 26;

FIG. 37 is an optical layout diagram illustrating an image displayapparatus according to further still another embodiment of the presentinvention;

FIG. 38 is an optical layout diagram illustrating a moving locus of eachof lens units constituting the projection optical system of FIG. 37during focusing;

FIG. 39 is a diagram illustrating an example of an image on a screen ina long distance projection period of the projection optical system ofFIG. 37;

FIG. 40A is a diagram illustrating distortion in the upper side of theimage exemplified in FIG. 39;

FIG. 40B is a diagram illustrating distortion in the left end of theimage exemplified in FIG. 39;

FIG. 40C is a diagram illustrating distortion in the lower end of theimage exemplified in FIG. 39;

FIG. 41 is a diagram illustrating an example of an image on a screen ina reference distance projection period of the projection optical systemof FIG. 37;

FIG. 42A is a diagram illustrating distortion in the upper side of theimage exemplified in FIG. 41;

FIG. 42B is a diagram illustrating distortion in the left end of theimage exemplified in FIG. 41;

FIG. 42C is a diagram illustrating distortion in the lower end of theimage exemplified in FIG. 41;

FIG. 43 is a diagram illustrating an example of an image on a screen ina close range projection period of the projection optical system of FIG.37;

FIG. 44A is a diagram illustrating distortion in the upper side of theimage exemplified in FIG. 43;

FIG. 44B is a diagram illustrating distortion in the left end of theimage exemplified in FIG. 43;

FIG. 44C is a diagram illustrating distortion in the lower end of theimage exemplified in FIG. 43;

FIG. 45 is a spot diagram in the long distance projection period of theprojection optical system of FIG. 37;

FIG. 46 is a spot diagram in the reference distance projection period ofthe projection optical system of FIG. 37;

FIG. 47 is a spot diagram in the close range projection period of theprojection optical system of FIG. 37;

FIG. 48 is a diagram illustrating field positions corresponding toangles of view of the image forming unit according to an embodiment ofthe present invention;

FIG. 49 is example mathematical formula representing an asphericalsurface and a free-form curved surface;

FIG. 50 is a table 1 illustrating examples of optical elements of theprojection optical system of FIG. 3;

FIG. 51 is a table 2 illustrating examples of lens intervals duringfocusing in the projection optical system of FIG. 3;

FIG. 52 is a table 3 illustrating examples of numerical values ofaspherical coefficients in the projection optical system of FIG. 3;

FIG. 53 is a table 4 illustrating examples of numerical values offree-form curved surface coefficients in the projection optical systemof FIG. 3;

FIG. 54 is a table 5 illustrating characteristics of an image formingunit of the projection optical system of FIG. 3;

FIG. 55 is a table 6 illustrating examples of position coordinates androtation angles of mirrors in the refraction optical system of FIG. 3;

FIGS. 56A and 56B are a table 7 illustrating examples of opticalelements of the projection optical system of FIG. 15;

FIG. 57 is a table 8 illustrating examples of lens intervals duringfocusing in the projection optical system of FIG. 15;

FIG. 58 is a table 9 illustrating examples of numerical values ofaspherical coefficients in the projection optical system of FIG. 15;

FIG. 59 is a table 10 illustrating examples of numerical values offree-form curved surface coefficients in the projection optical systemof FIG. 15;

FIG. 60 is a table 11 illustrating characteristics of an image formingunit of the projection optical system of FIG. 15;

FIG. 61 is a table 12 illustrating examples of position coordinates androtation angles of mirrors in the refraction optical system of FIG. 15;

FIGS. 62A and 62B are a table 13 illustrating examples of opticalelements of the projection optical system of FIG. 26;

FIG. 63 is a table 14 illustrating examples of lens intervals duringfocusing in the projection optical system of FIG. 26;

FIG. 64 is a table 15 illustrating examples of numerical values ofaspherical coefficients in the projection optical system of FIG. 26;

FIG. 65 is a table 16 illustrating examples of numerical values offree-form curved surface coefficients in the projection optical systemof FIG. 26;

FIG. 66 is a table 17 illustrating characteristics of an image formingunit of the projection optical system of FIG. 26;

FIG. 67 is a table 18 illustrating examples of position coordinates androtation angles of mirrors in the refraction optical system of FIG. 26;

FIGS. 68A and 68B are a table 19 illustrating examples of opticalelements of the projection optical system of FIG. 37;

FIG. 69 is a table 20 illustrating examples of lens intervals duringfocusing in the projection optical system of FIG. 37;

FIG. 70 is a table 21 illustrating examples of numerical values ofaspherical coefficients in the projection optical system of FIG. 37;

FIG. 71 is a table 22 illustrating examples of numerical values offree-form curved surface coefficients in the projection optical systemof FIG. 37;

FIG. 72 is a table 23 illustrating characteristics of an image formingunit of the projection optical system of FIG. 37;

FIG. 73 is a table 24 illustrating examples of position coordinates androtation angles of mirrors in the refraction optical system of FIG. 37;

FIG. 74 is a table 25 illustrating example numerical values representingthe condition in each one of the above-described examples; and

FIG. 75 is a table 26 illustrating example values representing eachcondition in each of the above-described examples.

DETAILED DESCRIPTION OF THE INVENTION

Hereinafter, a projection optical system and an image display apparatusaccording to embodiments of the present invention will be described withreference to the drawings. In the following, the image display apparatusis provided with the projection optical system, which projects an imageformed at an image forming unit on a projection plane.

First Embodiment of Image Display Apparatus

FIG. 1 is an optical layout diagram illustrating a projector 1, which isone example of image display apparatus. The projector 1 includes animage forming unit 10, a parallel plate 40, a projection optical system100, an illumination optical system 20 including a light source thatilluminates the image forming unit 10 with illumination light, and othermembers used for image formation, which may be accommodated in a housing30.

The image forming unit 10 may be implemented by any device capable offorming a to-be-projected image thereon, such as, a digital micromirrordevice (DMD), a transmission type liquid crystal panel, a reflectiontype liquid crystal panel, etc.

The parallel plate 40 is a cover glass (seal glass), which is arrangedin the vicinity of the image forming unit 10 to protect the imageforming unit 10.

The projection optical system 100 includes a refraction optical system101, a plane mirror 102 functioning as a first reflecting surface, and acurved mirror 103 functioning as a second reflecting surface. Asillustrated in FIG. 1, in this example, the plane mirror 102 is arrangedsuch that the normal line of the plane mirror 102 is rotated by 45degrees from the Z axis toward the Y axis direction on the YZ plane. Thecurved mirror 103 may be a concave mirror or a free-form curved surfacemirror of which reflecting surface has a shape of a free-form curvedsurface. Details of the projection optical system 100 will be describedlater.

The illumination optical system 20 includes, for example, a rodintegrator, a flyeye integrator, or the like in order to efficientlyperform uniform illumination on the image forming unit 10. In addition,the illumination optical system 20 is provided with a light source. Asthe light source, a white light source such as an ultra-high pressuremercury lamp, a xenon lamp, a halogen lamp, and a light-emitting diode(LED) or a monochromatic light source such as a monochromaticlight-emitting LED and a monochromatic light-emitting LD may be used.

In the below description, the image forming unit 10 is assumed to be an“image forming unit having no light-emission function” such as a DMD.However, the image forming unit applicable to this embodiment of thepresent invention is not limited thereto, but a “self-emission typeimage forming unit having a light-emission function of emitting light ona generated image” may be used.

The image forming unit 10 which is a DMD is illuminated withillumination light of the illumination optical system 20 and reflectsthe illumination light. Image information is formed by the reflectedlight. In other words, the image information generated by the DMD is aflux of light which is two-dimensionally intensity-modulated. The fluxof light becomes a flux of projection light as object light. The imageformed on the image forming unit 10 is magnified and projected on ascreen.

The screen may be arranged to be perpendicular to the image forming unit10. In other words, the normal line of an image formation plane of theimage forming unit 10 is perpendicular to the normal line of the screenas a projection plane.

An intermediate image which is conjugate with the image informationformed in the image forming unit 10 is formed by the light beam passingthrough the refraction optical system 101. The intermediate image isformed as a spatial image in the side closer to the image forming unit10 than the plane mirror 102. In addition, the intermediate image is notnecessarily formed as a plane image, but the intermediate image may beformed as a curved image.

The image is displayed on the screen by magnifying and projecting theintermediate image by using the curved mirror 103 which is arranged tobe closest to the magnification side in the projection optical system100. Although the intermediate image has a curvature of field ordistortion, the reflecting surface of the curved mirror 103 isconfigured to have a shape of a free-form curved surface, so that it ispossible to correct the curvature of field and the distortion.Accordingly, since a burden of aberration correction on the refractionoptical system 101 is reduced, a degree of freedom in the design of theprojection optical system 100 is increased, so that it is advantageousto miniaturization.

The refraction optical system 101 is configured so that the first lensunit 11 having a group of positive lenses, the plane mirror 102, and thecurved mirror 103 are fixed with respect to the image forming unit 10during focusing from a long distance side to a close range side. Thesecond lens unit 12 having a group of positive lenses and the third lensunit 13 having a group of negative lenses are moved to the magnificationside at one time and, after that, are moved to the image forming unit 10side. The fourth lens unit 14 having a group of positive lenses, ismoved to the magnification side during focusing from a long distanceside to a close range side. In other words, the projection opticalsystem 100 can control a curvature of field or distortion aberration ata high accuracy by performing floating focusing.

In the refraction optical system 101, an aspherical lens is arranged inthe lens unit which is moved during focusing. With this configuration,the effect of the correction is further improved.

The projector 1 illustrated in FIG. 1 is an image display apparatusaccording to Example 1 described below. FIG. 1 is also an optical pathdiagram illustrating a case of 48-inch projector where the front lenselements provided to the projection optical system 100 are drawn out tothe extreme degree. As clarified from FIG. 1, a sufficient intervalbetween each lens and each light beam is maintained, so thatinterference between each light beam and each lens or a lens barrel (notillustrated) can be avoided in this state.

Next, the image forming unit included in the projection optical systemaccording to an example embodiment of the present invention will bedescribed. FIG. 2 is a plan view illustrating the image forming unit 10according to the embodiment as seen from the image formation plane side.A plane in the image forming unit 10 on which the image information isformed is defined by an image formation plane. In FIG. 2, the imageforming unit 10 is shifted in the Y axis direction with respect to theoptical axis Lx described below. As illustrated in FIG. 2, theintersection of the Y direction axis line passing through a center C ofthe image forming unit 10 and the optical axis Lx is indicated by B0.The intersection of the Y direction axis line passing through the centerC of the image forming unit 10 and the end portion of the image formingunit 10 is indicated by L0. The maximum value of the distance betweenthe intersection B0 and the intersection L0 is denoted by a symbol“Ymax”. The distance Ymax is denoted by a maximum angle of view in the Yaxis direction.

Next, the projection optical system 100 according to the embodiment willbe described in more detail. FIGS. 3 and 4 are optical layout diagramsof the projection optical system 100. As illustrated in FIGS. 3 and 4,the projection optical system 100 includes the image forming unit 10,the refraction optical system 101, the plane mirror 102 which is a firstreflecting surface, and the curved mirror 103 which is a secondreflecting surface.

Next, symbols for describing relations between optical elements in thepresent disclosure will be described with reference to FIGS. 3 and 4.FIGS. 3 and 4 are optical path diagrams illustrating optical paths oflight beams projected from the image forming unit 10 to the screen.

As illustrated in FIGS. 3 and 4, an axis shared by the largest number oflenses among a plurality of the lenses constituting the refractionoptical system 101 is defined by the optical axis Lx. The directionparallel to the optical axis Lx is defined by the Z axis direction; andthe arrangement direction of the plane mirror 102 and the curved mirror103 is defined by the Y axis direction. In other words, the directionperpendicular to the optical axis Lx on the plane including the lightbeam path passing through the center C (refer to FIG. 2) of the imageforming unit 10, the center of a stop (not illustrated) included in therefraction optical system 101, and the center of the screen (notillustrated) is defined by the Y axis direction. In addition, thedirection perpendicular to the Y axis direction and the Z axis directionis defined by the X axis direction.

FIGS. 3 and 4 are also cross-sectional views of the projection opticalsystem 100 on the YZ plane. FIGS. 3 and 4 illustrate only the light beampaths parallel to the YZ plane among the light beams from the imageforming unit 10. In addition, in FIGS. 3 and 4, the rotation from the +Zaxis direction to the +Y axis direction on the YZ plane is defined by +αrotation.

As illustrated in FIG. 3, among lens surfaces of the lens which isarranged to be closest to the magnification side among the lensesincluded in the refraction optical system 101, the lens surface closerto the magnification side is denoted by “S1”. In focusing, a minimumvalue of the distance between the intersection of the lens surface S1and the optical axis Lx and the intersection of the plane mirror 102 andthe optical axis Lx is denoted by “L”. When the L has a minimum value,among the intersections of the plane mirror 102 and the light beam pathsparallel to the YZ cross section, the point on the plane mirror 102 ofwhich distance from the optical axis Lx has a maximum value is denotedby “H”. Among the intersections of the curved mirror 103 and the lightbeam paths parallel to the YZ cross section, the point on the curvedmirror 103 of which distance from the optical axis Lx has a minimumvalue is denoted by “F”. In addition, an angle between the segmentconnecting the point H and the point F and the optical axis Lx isdenoted by θ1.

Among the intersections of the light beam paths parallel to the YZ crosssection and the surface S1, the distance between the point on thesurface S1 of which distance from the optical axis Lx has a maximumvalue and the optical axis Lx is denoted by “D1”. Further, a sag amountof the surface S1 at the distance D1 from the top of the lens surface S1is denoted by “ds1”. The positive direction of the sag amount ds1 isdefined by the direction from the reduction side to the magnificationside. In other words, in this disclosure, the sag amount of the surfaceS1 may be referred to as a surface sag indicating the height of thesurface S1.

Among the light beams illustrated in FIG. 4, the light beam indicated bythe thick solid black line is an upper light beam at the maximum angleof view in the Y axis direction. The distance between the intersectionof the upper light beam and the surface S1 and the optical axis Lx isdenoted by “D2”. The sag amount of the surface S1 at the distance D2 isdenoted by “ds2”. Further, an angle between the light beam emitted fromthe refraction optical system 101 for the upper light beam and theoptical axis Lx is denoted by θ2.

Among the symbols described above, the meanings of the symbolsrepresenting the positional relation between the optical elementsconstituting the projector 1 are the same in each example describedbelow.

Next, specific numerical examples of the projection optical system 100will be described. First, meanings of symbols used in each example willbe described. The meanings of symbols are as follows.

f: focal distance of the entire system of the projection optical system100

NA: aperture efficiency

ω: half angle of view (deg)

R: radius of curvature (paraxial radius of curvature of an asphericsurface)

D: surface interval

Nd: refractive index

νd (Vd): Abbe number

K: conic constant of an aspheric surface

Ai: i-th order aspherical constant

Cj: free-form curved surface coefficient

C: reciprocal of paraxial radius of curvature (paraxial curvature)

H: height from optical axis

K: conic constant

A shape of an aspherical surface is represented as an aspherical amountX in the optical axis direction by the Mathematical Formula 1(Equation 1) illustrated in FIG. 49 using the paraxial curvature C, theheight H from the optical axis, the conic constant K, and the i-th orderaspherical constants Ai.

The shape of an aspherical surface is specified by applying the paraxialcurvature C, the conic constant K, and the aspherical constants Ai tothe aforementioned Mathematical Formula 1.

A shape of a free-form curved surface is expressed as a free-form curvedsurface amount X in the optical axis direction by the MathematicalFormula 2 (Equation 2) illustrated in FIG. 49 using the paraxialcurvature C, the height H from an optical axis, the conic constant K,and the free-form curved surface coefficients Cj. Herein, j isrepresented by the Mathematical Formula 3 (Equation 3) illustrated inFIG. 49.

The shape of a free-form curved surface is specified by applying theparaxial curvature C, the conic constant K, and the free-form curvedsurface coefficients Cj to the aforementioned Mathematical Formula 2.

Example 1

FIG. 5 is an optical layout diagram illustrating the refraction opticalsystem 101 according to this example. As illustrated in FIG. 5, therefraction optical system 101 includes a first lens unit 11, a secondlens unit 12, a third lens unit 13, and a fourth lens unit 14.

In FIG. 5, each solid line represents a moving locus of each of the lensunits constituting the refraction optical system 101 during focusingfrom a long distance side (far distance) to a close range side (neardistance). In addition, the long distance side is defined by the casewhere an image size projected on a screen is 80 inches; and the closerange side is defined by the case where the image size is 48 inches.

The first lens unit 11 is configured to include, in order from the imageforming unit 10 side, a both-side aspherical biconvex lens having astronger convex surface toward the image forming unit 10 side, anegative meniscus lens having a convex surface toward the image formingunit 10 side, a cemented lens of a biconvex lens having a strongerconvex surface toward the magnification side and a negative meniscuslens having a convex surface toward the magnification side, an aperturestop (not illustrated), a biconvex lens having a stronger convex surfacetoward the magnification side, a biconcave lens having a strongerconcave surface at the magnification side, a cemented lens of a positivemeniscus lens having a convex surface toward the magnification side anda negative meniscus lens having a convex surface toward themagnification side, and a biconvex lens having a stronger convex surfacetoward the magnification side.

The second lens unit 12 is configured with a positive meniscus lenshaving a convex surface toward the image forming unit 10 side.

The third lens unit 13 is configured to include a biconcave lens Bhaving a stronger concave surface toward the image forming unit 10 sideand a both-side aspherical biconcave lens A having a stronger concavesurface toward the image forming unit 10 side and having a shape thathas a negative power on the axis and a positive power in the periphery.

The fourth lens unit 14 is configured to include a both-side asphericalnegative meniscus lens having a convex surface toward the image formingunit 10 side and having a shape that has a negative power on the axisand a positive power in the periphery and a both-side asphericalbiconvex lens having a stronger convex surface toward the magnificationside and having a shape that has a positive power on the axis and anegative power in the periphery.

Table 1 illustrated in FIG. 50 lists data representing examples ofoptical elements included in the projection optical system 100 accordingto Example 1.

In the table, S denotes each lens surface of the refraction opticalsystem 101 as indicated by the numeral in FIG. 5. Further, a light beamdistance, or an optical length, denotes a distance between a lower lightbeam at the maximum angle of view in the Y axis direction on eachsurface and the optical axis Lx.

Table 2 illustrated in FIG. 51 represents a specific example of lensintervals during focusing in the projection optical system 100 accordingto this example.

Table 3 illustrated in FIG. 52 represents a specific example ofnumerical values of aspherical coefficients in the projection opticalsystem 100 according to this example. The aspherical surface isexpressed by the above-described Mathematical Formula 1 (Equation 1)illustrated in FIG. 49.

Table 4 illustrated in FIG. 53 represents a specific example ofnumerical values of free-form curved surface coefficients in theprojection optical system 100 according to this example. The free-formcurved surface is expressed by the above-described Mathematical Formula2 (Equation 2) illustrated in FIG. 49.

Table 5 illustrated in FIG. 54 represents a specific example of a DMDused as the image forming unit 10 in the projection optical system 100according to this example.

Table 6 illustrated in FIG. 55 represents a specific example of positioncoordinates and angles of α rotation of the plane mirror 102 and thecurved mirror 103 from the vertex of the lens located to be closest tothe plane mirror 102 side among the lenses included in the refractionoptical system 101 in the focus state where the projected image has amaximum size. The rotation represents the angle between the normal lineof the surface and the optical axis Lx.

Next, suppression of a deterioration in image quality at each projectiondistance in the projection optical system 100 according to the examplewill be described with reference to FIGS. 6 to 11C. FIGS. 6 to 11C arediagrams of images illustrating positions of main light beams having awavelength of 550 nm and diagrams illustrating distortion of an image ateach angle of view when the image representing the positions of the mainlight beams is displayed on the screen with respect to each zoomposition and each projection distance in the projection optical system100 according to Example 1.

FIG. 6 illustrates an example of an image representing positions ofspots having a wavelength of 550 nm displayed on the screen in theprojection optical system 100 in a long distance projection period. FIG.7A is a diagram illustrating distortion in the upper side of the imageexemplified in FIG. 6. FIG. 7B is a diagram illustrating distortion inthe left end of the image exemplified in FIG. 6. FIG. 7C is a diagramillustrating distortion in the lower end of the image exemplified inFIG. 6.

FIG. 8 illustrates an example of an image representing positions ofspots having a wavelength of 550 nm displayed on the screen in theprojection optical system 100 in a reference distance projection period.FIG. 9A is a diagram illustrating distortion in the upper side of theimage exemplified in FIG. 8. FIG. 9B is a diagram illustratingdistortion in the left end of the image exemplified in FIG. 8. FIG. 9Cis a diagram illustrating distortion in the lower end of the imageexemplified in FIG. 8.

FIG. 10 illustrates an example of an image representing positions ofspots having a wavelength of 550 nm displayed on the screen in theprojection optical system 100 in a close range projection period. FIG.11A is a diagram illustrating distortion in the upper side of the imageexemplified in FIG. 10. FIG. 11B is a diagram illustrating distortion inthe left end of the image exemplified in FIG. 10. FIG. 11C is a diagramillustrating distortion in the lower end of the image exemplified inFIG. 10.

Hereinbefore, as illustrated in FIGS. 6 to 11C, in the projectionoptical system 100 according to this example, it is possible to projectan image having small distortion with respect to each zoom position andeach projection distance.

Next, it is described that a change in an image is suppressed duringzooming at each angle of view by using spot diagrams in the projectionoptical system 100 according to the example with reference to FIGS. 12to 14. The spots in each of the spot diagrams illustrated in FIGS. 12 to14 correspond to field positions indicated by F1 to F13 illustrated inFIG. 48. Each spot diagram illustrates image formation characteristics(mm) on the screen plane with respect to wavelengths of 625 nm (red),550 nm (green), and 425 nm (blue).

FIG. 12 is a spot diagram in the long distance projection period. FIG.13 is a spot diagram in the reference distance projection period. FIG.14 is a spot diagram in the close range projection period.

As illustrated in FIGS. 12 to 14, according to the projection opticalsystem 100 of this example, a variation in image quality at each zoomposition and each projection distance is suppressed.

Second Embodiment of Image Display Apparatus

Next, another embodiment of the image display apparatus according to thepresent invention will be described. In the following description, thesame components are denoted by the same reference numerals, and thedetailed description thereof is not repeated.

FIG. 15 is an optical layout diagram illustrating a projector 1 aaccording to an embodiment of the present invention. In FIG. 15, theprojector 1 a includes the image forming unit 10, the parallel plate 40,a projection optical system 100 a, the illumination optical system 20including a light source which illuminates the image forming unit 10with illumination light, and other members used for image formation,which may be accommodated in the housing 30.

The projection optical system 100 a includes a refraction optical system101 a, a plane mirror 102 a which is a first reflecting surface, and acurved mirror 103 a which is a second reflecting surface. As illustratedin FIG. 15, the plane mirror 102 a is arranged such that the normal lineof the plane mirror 102 a is rotated by 45 degrees from the Z axistowards the Y axis direction on the YZ plane. The curved mirror 103 amay be a concave mirror or a free-form curved surface mirror of whichreflecting surface has a shape of a free-form curved surface.

As described above in the case of First Embodiment, the image formed onthe image forming unit 10 is magnified and projected on a screen (notillustrated).

The screen (not illustrated) is arranged to be perpendicular to theimage forming unit 10. In other words, the normal line of an imageformation plane of the image forming unit 10 is perpendicular to thenormal line of the screen as a projection plane.

An intermediate image which is conjugate with the image informationformed in the image forming unit 10 is formed by the light beam passingthrough the refraction optical system 101 a. The intermediate image isformed as a spatial image in the side closer to the image forming unit10 than the plane mirror 102 a. The intermediate image is notnecessarily formed as a plane image, but the intermediate image may beformed as a curved image.

The image is displayed on the screen by magnifying and projecting theintermediate image by using the curved mirror 103 a which is arranged tobe closest to the magnification side in the projection optical system100 a. Although the intermediate image has a curvature of field ordistortion, the reflecting surface of the curved mirror 103 a isconfigured to have a shape of a free-form curved surface, so that it ispossible to correct the curvature of field and the distortion.Accordingly, since a burden of aberration correction on the refractionoptical system 101 a is reduced, a degree of freedom in the design ofthe projection optical system 100 a is increased, so that it isadvantageous in miniaturization.

The refraction optical system 101 a is configured so that the first lensunit 11 a having a group of lenses with a positive refractive power, theplane mirror 102 a, and the curved mirror 103 a are fixed to the imageforming unit 10 during focusing from a long distance side to a closerange side. The second lens unit 12 a which is a lens unit having apositive refractive power and the third lens unit 13 a which is a lensunit having a negative refractive power are moved to the image formingunit 10 side. The fourth lens unit 14 a which is a lens unit having apositive refractive power is moved to the magnification side. In otherwords, the projection optical system 100 a can control a curvature offield or distortion aberration with high accuracy by performing floatingfocusing.

Further, since the refraction optical system 101 a is configured so thatan aspherical lens is arranged in the lens unit which is moved duringfocusing, it is possible to improve the effect of the correction.

The projector 1 a illustrated in FIG. 15 is an image display apparatusaccording to Example 2 described below. FIG. 15 is also an optical pathdiagram illustrating a case of 48-inch projector where the front lenselements provided to the projection optical system 100 a are drawn outto the extreme degree. In this disclosure, the front lens elementscorrespond to a lens which is arranged to be closest to themagnification side of the refraction optical system. As clarified fromFIG. 15, a sufficient interval between each lens and each light beam ismaintained, so that interference between each light beam and each lensor a lens barrel (not illustrated) can be avoided in this state.

Example 2

FIG. 16 is an optical layout diagram illustrating a refraction opticalsystem 101 a included in the projection optical system 100 a accordingto this example. As illustrated in FIG. 16, the refraction opticalsystem 101 a includes, in order from the image forming unit 10 side, afirst lens unit 11 a, a second lens unit 12 a, a third lens unit 13 a,and a fourth lens unit 14 a.

In FIG. 16, each solid line represents a moving locus of each of thelens units constituting the refraction optical system 101 a duringfocusing from a long distance side (far distance) to a close range side(near distance). In addition, the long distance side is defined by thecase where an image size projected on a screen is 80 inches; and theclose range side is defined by the case where the image size is 48inches.

The first lens unit 11 a is configured to include, in order from theimage forming unit 10 side, a both-side aspherical biconvex lens havinga stronger convex surface toward the image forming unit 10 side, anegative meniscus lens having a convex surface toward the image formingunit 10 side, a cemented lens of a biconvex lens having a strongerconvex surface toward the magnification side and a negative meniscuslens having a convex surface toward the magnification side, an aperturestop (not illustrated), a biconvex lens having a stronger convex surfacetoward the magnification side, a biconcave lens having a strongerconcave surface at the magnification side, a cemented lens of a positivemeniscus lens having a convex surface toward the magnification side anda negative meniscus lens having a convex surface toward the screen side,and a biconvex lens having a stronger convex surface toward themagnification side.

The second lens unit 12 a is configured with a positive meniscus lenshaving a convex surface toward the image forming unit 10 side.

The third lens unit 13 a is configured to include a negative meniscuslens Ba having a convex surface toward the magnification side and aboth-side aspherical biconcave lens Aa having a stronger concave surfacetoward the image forming unit 10 side and having a shape that has anegative power on the optical axis Lx and a positive power in theperiphery.

The fourth lens unit 14 a is configured to include a both-sideaspherical biconcave lens having a stronger concave surface toward theimage forming unit 10 side and having a shape that has a negative poweron the optical axis Lx and a positive power in the periphery and aboth-side aspherical biconvex lens having a stronger convex surfacetoward the magnification side and having a shape that has a positivepower on the optical axis Lx and a negative power in the periphery.

Table 7 (Tables 7A and 7B) illustrated in FIGS. 56A and 56B lists datarepresenting examples of optical elements included in the projectionoptical system 100 a of FIG. 15 according to Example 2. In the table, Sdenotes each lens surface of the refraction optical system 101 a asindicated by the numeral in FIG. 16. Further, a light beam distance, oran optical length, denotes a distance between a lower light beam at themaximum angle of view in the Y axis direction on each surface and theoptical axis Lx.

Table 8 illustrated in FIG. 57 represents a specific example of lensintervals during focusing in the projection optical system 100 aaccording to this example.

Table 9 illustrated in FIG. 58 represents a specific example ofnumerical values of aspherical coefficients in the projection opticalsystem 100 a according to this example. The aspherical surface isexpressed by the above-described Mathematical Formula 1 (Equation 1)illustrated in FIG. 49.

Table 10 illustrated in FIG. 59 represents a specific example ofnumerical values of free-form curved surface coefficients in theprojection optical system 100 a according to this example. The free-formcurved surface is expressed by the above-described Mathematical Formula2 (Equation 2) illustrated in FIG. 49.

Table 11 illustrated in FIG. 60 represents a specific example of a DMDused as the image forming unit 10 in the projection optical system 100 aaccording to this example.

Table 12 illustrated in FIG. 61 represents a specific example ofposition coordinates and angles of α rotation of the plane mirror 102 aand the curved mirror 103 a from the vertex of the lens located to beclosest to the plane mirror 102 a side among the lenses included in therefraction optical system 101 a in the focus state where the projectedimage has a maximum size. The rotation represents the angle between thenormal line of the surface and the optical axis Lx.

Next, suppression of a deterioration in image quality at each projectiondistance in the projection optical system 100 a according to thisexample will be described with reference to FIGS. 17 to 22C. FIGS. 17 to22C are diagrams illustrating positions of main light beams having awavelength of 550 nm and diagrams illustrating distortion of an image ateach angle of view when the image representing the positions of the mainlight beams is displayed on the screen with respect to each zoomposition and each projection distance in the projection optical system100 a according to Example 2.

FIG. 17 illustrates an example of an image representing positions ofspots having a wavelength of 550 nm displayed on the screen in theprojection optical system 100 a in a long distance projection period.FIG. 18A is a diagram illustrating distortion in the upper side of theimage exemplified in FIG. 17. FIG. 18B is a diagram illustratingdistortion in the left end of the image exemplified in FIG. 17. FIG. 18Cis a diagram illustrating distortion in the lower end of the imageexemplified in FIG. 17.

FIG. 19 illustrates an example of an image representing positions ofspots having a wavelength of 550 nm displayed on the screen in theprojection optical system 100 a in a reference distance projectionperiod. FIG. 20A is a diagram illustrating distortion in the upper sideof the image exemplified in FIG. 19. FIG. 20B is a diagram illustratingdistortion in the left end of the image exemplified in FIG. 19. FIG. 20Cis a diagram illustrating distortion in the lower end of the imageexemplified in FIG. 19.

FIG. 21 illustrates an example of an image representing positions ofspots having a wavelength of 550 nm displayed on the screen in theprojection optical system 100 a in a close range projection period. FIG.22A is a diagram illustrating distortion in the upper side of the imageexemplified in FIG. 21. FIG. 22B is a diagram illustrating distortion inthe left end of the image exemplified in FIG. 21. FIG. 22C is a diagramillustrating distortion in the lower end of the image exemplified inFIG. 21.

Hereinbefore, as illustrated in FIGS. 17 to 22C, according to theprojection optical system 100 a of Example 2, it is possible to projectan image having small distortion with respect to each zoom position andeach projection distance.

Next, suppression of a change in an image during zooming at each angleof view by using spot diagrams in the projection optical system 100 aaccording to this example will be described. The spots in each of spotdiagrams illustrated in FIGS. 23 to 25 correspond to field positionsindicated by F1 to F13 illustrated in FIG. 48. Each spot diagramillustrates image formation characteristics (mm) on the screen planewith respect to wavelengths of 625 nm (red), 550 nm (green), and 425 nm(blue).

FIG. 23 is a spot diagram in the long distance projection period. FIG.24 is a spot diagram in the reference distance projection period. FIG.25 is a spot diagram in the close range projection period.

As illustrated in FIGS. 23 to 25, according to the projection opticalsystem 100 a of this example, a variation in image quality at each zoomposition and each projection distance is suppressed.

Third Embodiment of Image Display Apparatus

Next, still another embodiment of the image display apparatus accordingto the present invention will be described. In the followingdescription, the same components are denoted by the same referencenumerals, and the detailed description thereof is not repeated.

FIG. 26 is an optical layout diagram illustrating a projector 1 baccording to an embodiment of the present invention. In FIG. 26, theprojector 1 b includes the image forming unit 10, th parallel plate 40,a projection optical system 100 b, th illumination optical system 20including a light source which illuminates the image forming unit 10with illumination light, and other members used for image formation,which may be accommodated in the housing 30.

The projection optical system 100 b includes a refraction optical system101 b, a plane mirror 102 b which is a first reflecting surface, and acurved mirror 103 b which is a second reflecting surface. As illustratedin FIG. 26, the plane mirror 102 b is arranged such that the normal lineof the plane mirror 102 b is rotated by 45 degrees from the Z axistowards the Y axis direction on the YZ plane. The curved mirror 103 bmay be a concave mirror or a free-form curved surface mirror of whichreflecting surface has a shape of a free-form curved surface.

As described above in the case of First Embodiment, the image formed onthe image forming unit 10 is magnified and projected on a screen (notillustrated).

The screen (not illustrated) is arranged to be perpendicular to theimage forming unit 10. In other words, the normal line of an imageformation plane of the image forming unit 10 is perpendicular to thenormal line of the screen as a projection plane.

An intermediate image which is conjugate with the image informationformed in the image forming unit 10 is formed by the light beam passingthrough the refraction optical system 101 b. The intermediate image isformed as a spatial image in the side closer to the image forming unit10 than the plane mirror 102 b. The intermediate image is notnecessarily formed as a plane image, but the intermediate image may beformed as a curved image.

The image is displayed on the screen by magnifying and projecting theintermediate image by using the curved mirror 103 b which is arranged tobe closest to the magnification side in the projection optical system100 b. Although the intermediate image has a curvature of field ordistortion, the reflecting surface of the curved mirror 103 b isconfigured to have a shape of a free-form curved surface, so that it ispossible to correct the curvature of field and the distortion.Accordingly, since a burden of aberration correction on the refractionoptical system 101 b is reduced, a degree of freedom in the design ofthe projection optical system 100 b is increased, so that it isadvantageous to miniaturization.

The refraction optical system 101 b is configured so that the first lensunit 11 b which is a lens unit having a positive refractive power, theplane mirror 102 b, and the curved mirror 103 b are fixed with respectto the image forming unit 10 during focusing from a long distance sideto a close range side. The second lens unit 12 b which is a lens unithaving a positive refractive power and the third lens unit 13 b which isa lens unit having a negative refractive power are moved to the imageforming unit 10 side. The fourth lens unit 14 b which is a lens unithaving a positive refractive power is moved to the magnification side.In other words, the projection optical system 100 can control acurvature of field or distortion aberration at a high accuracy byperforming floating focusing.

Further, since the refraction optical system 101 b is configured so thatan aspherical lens is arranged in the lens unit which is moved duringfocusing, it is possible to improve the effect of the correction.

The projector 1 b illustrated in FIG. 26 is an image display apparatusaccording to Example 3 described below. FIG. 26 is also an optical pathdiagram illustrating a case of 48-inch projector where the front lenselements provided to the projection optical system 100 b are drawn outto the extreme degree. As clarified from FIG. 26, a sufficient intervalbetween each lens and each light beam is maintained, so thatinterference between each light beam and each lens or a lens barrel (notillustrated) can be avoided in this state.

Example 3

FIG. 27 is an optical layout diagram illustrating a refraction opticalsystem 101 b included in the projection optical system 100 b accordingto this example. As illustrated in FIG. 27, the refraction opticalsystem 101 b includes, in order from the image forming unit 10 side, afirst lens unit 11 b, a second lens unit 12 b, a third lens unit 13 b,and a fourth lens unit 14 b.

In FIG. 27, each solid line represents a moving locus of each of thelens units constituting the refraction optical system 101 b duringfocusing from a long distance side (far distance) to a close range side(near distance). In addition, the long distance side is defined by thecase where an image size projected on a screen is 80 inches; and theclose range side is defined by the case where the image size is 48inches.

The first lens unit 11 b is configured to include, in order from theimage forming unit 10 side, a both-side aspherical biconvex lens havinga stronger convex surface toward the image forming unit 10 side, anegative meniscus lens having a convex surface toward the image formingunit 10 side, a cemented lens of a negative meniscus lens having aconvex surface toward the image forming unit 10 side and a biconvex lenshaving a stronger convex surface toward the image forming unit 10 side,an aperture stop (not illustrated), a both-side aspherical convex lenshaving a stronger convex surface toward the magnification side, abiconcave lens having a stronger concave surface at the magnificationside, a cemented lens of a positive meniscus lens having a convexsurface toward the magnification side and a negative meniscus lenshaving a convex surface toward the magnification side, and a biconvexlens having a stronger convex surface toward the magnification side.

The second lens unit 12 b is configured with a positive meniscus lenshaving a convex surface toward the image forming unit 10 side.

The third lens unit 13 b is configured to include a negative meniscuslens Bb having a convex surface toward the magnification side and aboth-side aspherical biconcave lens Ab having a stronger concave surfacetoward the image forming unit 10 side and having a shape that has anegative power on the optical axis Lx and a positive power in theperiphery.

The fourth lens unit 14 b is configured to include a both-sideaspherical negative meniscus lens having a convex surface toward themagnification side and having a shape that has a negative power on theoptical axis Lx and a positive power in the periphery and a both-sideaspherical positive meniscus lens having a convex surface toward themagnification side and having a shape that has a positive power on theoptical axis Lx and a negative power in the periphery.

Table 13 (Tables 13A and 13B) of FIGS. 62A and 62B lists datarepresenting examples of optical elements included in the projectionoptical system 100 b according to Example 3. In the table, S denoteseach lens surface of the refraction optical system 101 b as indicated bythe numeral in FIG. 27. Further, a light beam distance denotes adistance between a lower light beam at the maximum angle of view in theY axis direction on each surface and the optical axis Lx.

Table 14 illustrated in FIG. 63 represents a specific example of lensintervals during focusing in the projection optical system 100 baccording to this example.

Table 15 illustrated in FIG. 64 represents a specific example ofnumerical values of aspherical coefficients in the projection opticalsystem 100 b according to this example. The aspherical surface isexpressed by the above-described Mathematical Formula 1 (Equation 1) ofFIG. 49.

Table 16 illustrated in FIG. 65 represents a specific example ofnumerical values of free-form curved surface coefficients in theprojection optical system 100 b according to this example. The free-formcurved surface is expressed by the above-described Mathematical Formula2 (Equation 2) illustrated in FIG. 49.

Table 17 represents a specific example of a DMD used as the imageforming unit 10 in the projection optical system 100 b according to thisexample.

Table 18 represents a specific example of position coordinates andangles of a rotation of the plane mirror 102 b and the curved mirror 103b from the vertex of the lens located to be closest to the plane mirror102 b side among the lenses included in the refraction optical system101 b in the focus state where the projected image has a maximum size.The rotation represents the angle between the normal line of the surfaceand the optical axis Lx.

Next, suppression of a deterioration in image quality at each zoomposition and each projection distance in the projection optical system100 b according to this example will be described with reference toFIGS. 28 to 33C. FIGS. 28 to 33C are diagrams illustrating positions ofmain light beams having a wavelength of 550 nm and diagrams illustratingdistortion of an image at each angle of view when the image representingthe positions of the main light beams is displayed on the screen withrespect to each zoom position and each projection distance in theprojection optical system 100 b according to Example 3.

FIG. 28 illustrates an example of an image representing positions ofspots having a wavelength of 550 nm displayed on the screen in theprojection optical system 100 b in a long distance projection period.FIG. 29A is a diagram illustrating distortion in the upper side of theimage exemplified in FIG. 28. FIG. 29B is a diagram illustratingdistortion in the left end of the image exemplified in FIG. 28. FIG. 29Cis a diagram illustrating distortion in the lower end of the imageexemplified in FIG. 28.

FIG. 30 illustrates an example of an image representing positions ofspots having a wavelength of 550 nm displayed on the screen in theprojection optical system 100 b in a reference distance projectionperiod. FIG. 31A is a diagram illustrating distortion in the upper sideof the image exemplified in FIG. 30. FIG. 31B is a diagram illustratingdistortion in the left end of the image exemplified in FIG. 30. FIG. 31Cis a diagram illustrating distortion in the lower end of the imageexemplified in FIG. 30.

FIG. 32 illustrates an example of an image representing positions ofspots having a wavelength of 550 nm displayed on the screen in theprojection optical system 100 b in a close range projection period. FIG.33A is a diagram illustrating distortion in the upper side of the imageexemplified in FIG. 32. FIG. 33B is a diagram illustrating distortion inthe left end of the image exemplified in FIG. 32. FIG. 33C is a diagramillustrating distortion in the lower end of the image exemplified inFIG. 32.

Hereinbefore, as illustrated in FIGS. 28 to 33C, according to theprojection optical system 100 b of this example, it is possible toproject an image having small distortion with respect to each zoomposition and each projection distance.

Next, suppression of a change in an image during zooming at each angleof view by using spot diagrams in the projection optical system 100 baccording to this example will be described. The spots in each of spotdiagrams illustrated in FIGS. 34 to 36 correspond to field positionsindicated by F1 to F13 illustrated in FIG. 48. Each spot diagramillustrates image formation characteristics (mm) on the screen planewith respect to wavelengths of 625 nm (red), 550 nm (green), and 425 nm(blue).

FIG. 34 is a spot diagram in the long distance projection period. FIG.35 is a spot diagram in the reference distance projection period. FIG.36 is a spot diagram in the close range projection period.

As illustrated in FIGS. 34 to 36, according to the projection opticalsystem 100 b of this example, a variation in image quality at each zoomposition and each projection distance is suppressed.

Fourth Embodiment of Image Display Apparatus

Next, further still another embodiment of the image display apparatusaccording to the present invention will be described. In the followingdescription, the same components are denoted by the same referencenumerals, and the detailed description thereof is not repeated.

FIG. 37 is an optical layout diagram illustrating a projector 1 caccording to an embodiment of the present invention. In FIG. 37, theprojector 1 c includes the image forming unit 10, the parallel plate 40,a projection optical system 100 c, the illumination optical system 20including a light source which illuminates the image forming unit 10with illumination light, and other members used for image formation,which may be accommodated in the housing 30.

The projection optical system 100 c is configured to include arefraction optical system 101 c, a plane mirror 102 c which is a firstreflecting surface, and a curved mirror 103 c which is a secondreflecting surface. As illustrated in FIG. 37, the plane mirror 102 c isarranged such that the normal line of the plane mirror 102 c is beingrotated by 45 degrees from the Z axis towards the Y axis direction onthe YZ plane. The curved mirror 103 c may be a concave mirror or afree-form curved surface mirror of which reflecting surface has a shapeof a free-form curved surface.

As described above in the case of Example 1, the image formed on theimage forming unit 10 is magnified and projected on a screen (notillustrated).

The screen (not illustrated) is arranged to be perpendicular to theimage forming unit 10. In other words, the normal line of an imageformation plane of the image forming unit 10 is perpendicular to thenormal line of the screen as a projection plane.

An intermediate image which is conjugate with the image informationformed in the image forming unit 10 is formed by the light beam passingthrough the refraction optical system 101 c. The intermediate image isformed as a spatial image in the side closer to the image forming unit10 than the plane mirror 102 c. In addition, the intermediate image isnot necessarily formed as a plane image, but the intermediate image maybe formed as a curved image.

The image is displayed on the screen by magnifying and projecting theintermediate image by using the curved mirror 103 c which is arranged tobe closest to the magnification side in the projection optical system100 c. Although the intermediate image has a curvature of field ordistortion, the reflecting surface of the curved mirror 103 c isconfigured to have a shape of a free-form curved surface, so that it ispossible to correct the curvature of field and the distortion.Accordingly, since a burden of aberration correction on the refractionoptical system 101 c is reduced, a degree of freedom in the design ofthe projection optical system 100 c is increased, so that it isadvantageous to miniaturization.

The refraction optical system 101 c is configured so that the first lensunit 11 c which is a lens unit having a positive refractive power, theplane mirror 102 c, and the curved mirror 103 c are fixed with respectto the image forming unit 10 during focusing from a long distance sideto a close range side. The second lens unit 12 c which is a lens unithaving a positive refractive power and the third lens unit 13 c which isa lens unit having a negative refractive power are moved to the imageforming unit 10 side. The fourth lens unit 14 c which is a lens unithaving a positive refractive power is moved to the magnification side.In other words, the projection optical system 100 c can control acurvature of field or distortion aberration at a high accuracy byperforming floating focusing.

In addition, since the refraction optical system 101 c is configured sothat an aspherical lens is arranged in the lens unit which is movedduring focusing, it is possible to improve the effect of the correction.

The projector 1 c illustrated in FIG. 37 is an image display apparatusaccording to Example 4 described below. FIG. 37 is also an optical pathdiagram illustrating a case of 48-inch projector where the front lenselements provided to the projection optical system 100 c are drawn outto the extreme degree. As clarified from FIG. 37, a sufficient intervalbetween each lens and each light beam is maintained, so thatinterference between each light beam and each lens or a lens barrel (notillustrated) can be avoided in this state.

Example 4

FIG. 38 is an optical layout diagram illustrating a refraction opticalsystem 101 c included in the projection optical system 100 c accordingto this embodiment. As illustrated in FIG. 38, the refraction opticalsystem 101 c is configured to include, in order from the image formingunit 10 side, a first lens unit 11 c, a second lens unit 12 c, a thirdlens unit 13 c, and a fourth lens unit 14 c.

In FIG. 38, each solid line represents a moving locus of each of thelens units constituting the refraction optical system 101 c duringfocusing from a long distance side (far distance) to a close range side(near distance). In addition, the long distance side is defined by thecase where an image size projected on a screen is 80 inches; and theclose range side is defined by the case where the image size is 48inches.

The first lens unit 11 c is configured to include, in order from theimage forming unit 10 side, a both-side aspherical biconvex lens havinga stronger convex surface toward the image forming unit 10 side, anegative meniscus lens having a stronger convex surface toward the imageforming unit 10 side, a cemented lens of a negative meniscus lens havinga convex surface toward the image forming unit 10 side and a biconvexlens having a stronger convex surface toward the magnification side, anaperture stop (not illustrated), a both-side aspherical convex lenshaving a stronger convex surface toward the magnification side, aboth-side aspherical biconvex lens having a stronger convex surface atthe magnification side, a biconcave lens having a stronger concavesurface at the magnification side, a cemented lens of a positivemeniscus lens having a convex surface toward the magnification side anda negative meniscus lens having a convex surface toward themagnification side, and a biconvex lens having a stronger convex surfacetoward the magnification side.

The second lens unit 12 c is configured with a positive meniscus lenshaving a convex surface toward the image forming unit 10 side.

The third lens unit 13 c is configured to include a negative meniscuslens Bc having a convex surface toward the magnification side and aboth-side aspherical biconcave lens Ac having a stronger concave surfacetoward the image forming unit 10 side and having a shape that has anegative power on the optical axis Lx and a positive power in theperiphery.

The fourth lens unit 14 c is configured to include a both-sideaspherical negative meniscus lens having a convex surface toward themagnification side and having a shape that has a negative power on theoptical axis Lx and a positive power in the periphery and a both-sideaspherical positive meniscus lens having a convex surface toward themagnification side and having a shape that has a positive power on theoptical axis Lx and a negative power in the periphery.

Table 19 (Tables 19A and 19B) illustrated in FIGS. 68A and 68B listsdata representing examples of optical elements included in theprojection optical system 100 c according to this example. In the table,S denotes each lens surface of the refraction optical system 101 c asindicated by the numeral in FIG. 38. Further, a light beam distance, oran optical length, denotes a distance between a lower light beam at themaximum angle of view in the Y axis direction on each surface and theoptical axis Lx.

Table 20 illustrated in FIG. 69 represents a specific example of lensintervals during focusing in the projection optical system 100 caccording to this example.

Table 21 illustrated in FIG. 70 represents a specific example ofnumerical values of aspherical coefficients in the projection opticalsystem 100 c according to this example. The aspherical surface isexpressed by the above-described Mathematical Formula 1 (Equation 1)illustrated in FIG. 49.

Table 22 illustrated in FIG. 71 represents a specific example ofnumerical values of free-form curved surface coefficients in theprojection optical system 100 c according to this example. The free-formcurved surface is expressed by the above-described Mathematical Formula2 (Equation 2) illustrated in FIG. 49.

Table 23 illustrated in FIG. 72 represents a specific example of a DMDused as the image forming unit 10 in the projection optical system 100 caccording to this example.

Table 24 illustrated in FIG. 73 represents a specific example ofposition coordinates and angles of α rotation of the plane mirror 102 cand the curved mirror 103 c from the vertex of the lens located to beclosest to the plane mirror 102 c side among the lenses included in therefraction optical system 101 c in the focus state where the projectedimage has a maximum size. The rotation represents the angle between thenormal line of the surface and the optical axis Lx.

Next, suppression of a deterioration in image quality at each zoomposition and each projection distance in the projection optical system100 c according to this example will be described with reference toFIGS. 39 to 44C. FIGS. 39 to 44C are diagrams illustrating positions ofmain light beams having a wavelength of 550 nm and diagrams illustratingdistortion of an image at each angle of view when the image representingthe positions of the main light beams is displayed on the screen withrespect to each zoom position and each projection distance in theprojection optical system 100 c according to Example 4.

FIG. 39 illustrates an example of an image representing positions ofspots having a wavelength of 550 nm displayed on the screen in theprojection optical system 100 c in a long distance projection period.FIG. 40A is a diagram illustrating distortion in the upper side of theimage exemplified in FIG. 39. FIG. 40B is a diagram illustratingdistortion in the left end of the image exemplified in FIG. 39. FIG. 40Cis a diagram illustrating distortion in the lower end of the imageexemplified in FIG. 39.

FIG. 41 illustrates an example of an image representing positions ofspots having a wavelength of 550 nm displayed on the screen in theprojection optical system 100 c in a reference distance projectionperiod. FIG. 42A is a diagram illustrating distortion in the upper sideof the image exemplified in FIG. 41. FIG. 42B is a diagram illustratingdistortion in the left end of the image exemplified in FIG. 41. FIG. 42Cis a diagram illustrating distortion in the lower end of the imageexemplified in FIG. 41.

FIG. 43 illustrates an example of an image representing positions ofspots having a wavelength of 550 nm displayed on the screen in theprojection optical system 100 c in a close range projection period. FIG.44A is a diagram illustrating distortion in the upper side of the imageexemplified in FIG. 43. FIG. 44B is a diagram illustrating distortion inthe left end of the image exemplified in FIG. 43. FIG. 44C is a diagramillustrating distortion in the lower end of the image exemplified inFIG. 43.

Hereinbefore, as illustrated in FIGS. 39 to 44C, according to theprojection optical system 100 c of this example, it is possible toproject an image having small distortion with respect to each zoomposition and each projection distance.

Next, suppression of a change in an image during zooming at each angleof view by using spot diagrams in the projection optical system 100 caccording to the example will be described. The spots in each of spotdiagrams illustrated in FIGS. 45 to 47 correspond to field positionsindicated by F1 to F13 illustrated in FIG. 48. Each spot diagramillustrates image formation characteristics (mm) on the screen planewith respect to wavelengths of 625 nm (red), 550 nm (green), and 425 nm(blue).

FIG. 45 is a spot diagram in the long distance projection period. FIG.46 is a spot diagram in the reference distance projection period. FIG.47 is a spot diagram in the close range projection period.

As illustrated in FIGS. 45 and 46, according to the projection opticalsystem 100 c of this example, a variation in image quality at each zoomposition and each projection distance is suppressed.

Now, main features of the above-described projection optical systems andimage display apparatuses according to the present invention are asfollows.

Feature 1

According to example embodiments of the present invention, there isprovided a projection optical system including: in order from areduction side to a magnification side, an image forming unit, arefraction optical system, and a first reflecting surface and a secondreflecting surface. When an optical axis shared by the largest number oflenses among optical axes of a plurality of the lenses of the refractionoptical system is defined by an optical axis of the projection opticalsystem, when, in arrangement where a distance between an intersection ofa magnification-side surface of a lens which is arranged to be closestto the magnification side of the refraction optical system and theoptical axis and an intersection between the first reflecting surfaceand the optical axis has a minimum value, the distance between theintersections is denoted by L, when a focal length of the refractionoptical system is denoted by f, when a direction parallel to the opticalaxis is defined by a Z axis direction, when an arrangement direction ofthe first reflecting surface and the second reflecting surface isdefined by a Y axis direction, and when a maximum value of a distancebetween the optical axis and an end portion of the image forming unit inthe Y axis direction is denoted by Ymax, in a YZ plane which is a planeparallel to the Y axis direction and the Z axis direction, a maximumvalue D1 of a distance between an intersection of a light beam from theimage forming unit and the magnification-side surface of the lens whichis arranged to be closest to the magnification side of the refractionoptical system and the optical axis, a sag amount ds1 which is a sagamount of the magnification-side surface of the lens which is arrangedto be closest to the magnification side of the refraction optical systemat the D1 and of which positive direction is defined by the directionfrom the reduction side in the Z axis toward the magnification side, apoint H of which distance from the optical axis has a maximum valueamong the intersections of the light beam and the first reflectingsurface, a point F of which distance from the optical axis has a minimumvalue among the intersections of the light beam and the secondreflecting surface, and an angle θ1 between a line connecting the H andthe F and the optical axis satisfies the following conditions (1) and(2).0<Ymax/f−1/tan θ1  condition (1)−0.1<(L−D1−ds1)/(L+D1−ds1)−1/tan θ1  condition (2)

In the projection optical system using mirrors, a method of inserting afolding mirror between the refraction optical system and the reflectionsurface is used in order to reduce a full-length direction size thereof.However, if conditions are not appropriate, interference occurs betweenthe light beam and the lens or a barrel member. As a method of avoidingthe interference (interference between the light beam and the member),there is a method of increasing a separation distance between thefolding mirror and the refraction optical system or a method of reducinga diameter of the lens which is closest to the magnification side of therefraction optical system. However, the former method is contrary to thepurpose of miniaturization in the full-length direction. In addition, inthe latter method, since the role of the lens such as aberrationcorrection, particularly, correction of a curvature of field ordistortion aberration is decreased, the burden to the second reflectingsurface is increased, so that the mirror size is increased. As a result,the size of the apparatus on which the projection optical system ismounted needs to be increased. In this manner, there is a problem inthat, if the size in the full-length direction is tried to be reducedwithout any preparation, performance is easily deteriorated, and if theperformance is tried to be secured, the size is increased.

With respect to the problem, according to the projection optical systemsatisfying the conditions (1) and (2), it is possible to provide aprojection optical system having a small size, having no occurrence ofinterference with a light beam, and having high performance. Each of theaforementioned conditions (1) and (2) represents an appropriate range ofan emission angle of the folded light beam from the first reflectingsurface.

If the aforementioned value is less than the lower limit of thecondition (1), interference easily occurs between the light emitted fromthe first reflecting surface and the lens, so that the emission angle ofthe light emitted from the refraction optical system is also increased.Accordingly, the size of the folding mirror becomes large, and thus, anintermediate image becomes large, so that the second reflecting surfaceneeds to be large. As a result, the image display apparatus on which theprojection optical system is mounted needs to be large.

In addition, in order to project an image at an appropriate position onthe screen, a radius of curvature of the second reflecting surface needsto be small. Accordingly, in the correction of the curvature of fieldand the distortion aberration, it is difficult to maintain balance, sothat a manufacturing error sensitivity of the second reflecting surfaceis increased or the performance is deteriorated.

In addition, if the aforementioned value is less than the lower limit ofthe condition (2), interference occurs between the lens and the lightbeam.

Therefore, when the conditions (1) and (2) are satisfied at the sametime, although the distance between the refraction optical system andthe first reflecting surface is shortened, the interference of the lightbeam does not occur, and the diameter of the lens which is closest tothe magnification side of the refraction optical system can beincreased. Accordingly, the burden to the lens, particularly, the roleof the correction of the curvature of field is increased, so that theburden to the second reflecting surface can be reduced.

In addition to the decrease in the manufacturing error sensitivity andthe improvement of the performance, the miniaturization of the secondreflecting surface and the miniaturization of the apparatus can beparticularly effectively implemented.

Feature 2

In the projection optical system according to the present invention, inaddition to Feature 1, when an angle between a light beam emitted fromthe refraction optical system for an upper light beam at the maximumangle of view in the Y axis direction and the optical axis is denoted byθ2, when a distance between an intersection of the light beam emittedfrom the refraction optical system for the upper light beam at themaximum angle of view in the Y axis direction and theclosest-magnification-side surface of the refraction optical system andthe optical axis is denoted by D2, and when a sag amount which is a sagamount of the magnification-side surface of the lens which is arrangedto be closest to the magnification side of the refraction optical systemat a height of the D2 and of which positive direction is defined by thedirection from the reduction side in the Z axis toward the magnificationside is denoted by ds2, the angle θ2 satisfies the following conditions(3) and (4).0<Ymax/f−1/tan θ2.  condition (3)−0.05<(L−D2−ds2)/(L+D1−ds2)−1/tan θ2.  condition (4)

Each of the conditions (3) and (4) represents an appropriate range ofthe emission angle of the upper light beam at the maximum angle in the Yaxis direction.

If the aforementioned value is less than the lower limit of thecondition (3), the emission angle of the upper light beam is increased,and thus, the size of the folding mirror becomes large, and theintermediate image becomes large. If the intermediate image becomeslarge, the second reflecting surface becomes large, so that theprojection optical system becomes large. In addition, since the anglebetween the light beam emitted from the first reflecting surface and theoptical axis is decreased, the interference of the lens easily occurs.In addition, in order to project an image at an appropriate position onthe screen, a radius of curvature of the second reflecting surface needsto be small. Accordingly, in the correction of the curvature of fieldand the distortion aberration, it is difficult to maintain balance, sothat a manufacturing error sensitivity of the second reflecting surfaceis increased or the performance is deteriorated.

If the aforementioned value is less than the lower limit of thecondition (4), interference occurs between the lens and the light beam.

Therefore, when the conditions (3) and (4) are satisfied at the sametime, although the distance between the refraction optical system andthe first reflecting surface is shortened, the interference of the lightbeam does not occur, and the diameter of the lens which is closest tothe magnification side of the refraction optical system can beincreased. Accordingly, the burden to the lens, particularly, the roleof the correction of the curvature of field is increased, so that theburden to the second reflecting surface can be reduced. In addition, themanufacturing error sensitivity is decreased, the performance isimproved, and the miniaturization of the second reflecting surface andthe miniaturization of the apparatus can be particularly effectivelyimplemented.

Feature 3

In the projection optical system according to example embodiments of thepresent invention, in addition to Features 1 and 2, a magnification-sidesurface of the lens which is arranged to be closest to the magnificationside of the refraction optical system is a convex and asphericalsurface.

According to the feature, since the closest-magnification-side lens isconfigured to have a convex surface, the effect of deflection of themain light beam is improved, so that the intermediate image can besmall. Therefore, the first reflecting surface and the second reflectingsurface can be miniaturized. In addition, the interference between thelens and the light beam can be easily avoided. In addition, since theclosest-magnification-side lens is configured to have an asphericalsurface, the effect of deflection of the main light beam and the effectof correction of the curvature of field can be improved.

Feature 4

In the projection optical system according to example embodiments of thepresent invention, in addition to Features 1 to 3, the projectionoptical system further includes a both-side aspherical biconcave lens Ahaving a negative power on the optical axis and a positive power in theperiphery.

Since the lens has a convex power in the periphery, an emission angle ofthe main light beam of off-axis light emitted from the refractionoptical system can be reduced, the miniaturization and the highperformance of the apparatus can be implemented. Preferably, theaspherical lens is different from the aspherical lens having a convexshape, which is described above referring to Feature 3. Alternatively,the aspherical lens may be the same as the aspherical lens having aconvex shape. Since a plurality of aspherical surfaces are used, it ispossible to control the distortion aberration and the curvature of fieldat a high accuracy, and it is possible to implement a high-performanceprojection optical system in combination with the effect of the concavemirror.

Feature 5

In the projection optical system according to example embodiments of thepresent invention, in addition to Features 1 to 4, the aspherical lensis arranged between a spherical lens of which distance between anintersection of a lower light beam at the maximum angle of view in the Yaxis direction and a surface and the optical axis is at maximum, and thefirst reflecting surface.

According to the feature, it is possible to control distortion and acurvature of field at a high accuracy by using the aspherical lens asdescribed above in a portion where light beams are sufficientlyseparated.

Feature 6

In the projection optical system according to example embodiments of thepresent invention, in addition to Features 1 to 5, the first reflectingsurface is a plane mirror and is rotated by 45 degrees on the YZ plane.

Herein, the 45 degrees represent that the normal line of the planemirror is rotated by 45 degrees (−45 degrees in the α direction) fromthe Z axis toward the Y axis direction. According to the feature, sincethe optical system can be folded and bended by 90 degrees without anychange in performance, the miniaturization can be effectivelyimplemented.

Feature 7

In the projection optical system according to example embodiments of thepresent invention, in addition to Features 1 to 6, the second reflectingsurface is a concave mirror.

According to the feature, since the intermediate image of the refractionoptical system is magnified and projected by the concave mirror, theminiaturization of the projection optical system can be implemented.

Feature 8

In the projection optical system according to example embodiment of thepresent invention, in addition to Features 1 to 7, in a focus statewhere the L is at minimum, when paraxial magnification of the refractionoptical system is denoted by β, the following condition (5) issatisfied.5<β<8.  condition (5)

The condition (5) is a mathematical formula for specifying anappropriate range of the size of the intermediate image. If theaforementioned value is more than the upper limit of the condition (5),the power of the concave mirror can be decreased, and thus, themanufacturing error sensitivity is reduced. However, since the size ofthe concave mirror is increased, the miniaturization cannot beimplemented.

In addition, if the aforementioned value is less than the lower limit ofthe condition (5), the miniaturization can be effectively implemented.However, the power of the concave mirror needs to be increased in orderto obtain a desired size of the projection image, and thus, themanufacturing error sensitivity needs to be increased. In addition, morepreferably, the following condition (5′) is satisfied.6<β<7.  condition (5′)

Feature 9

In the projection optical system according to example embodiments of thepresent invention, in addition to Features 1 to 8, the second reflectingsurface has a shape of a free-form curved surface.

Since the second reflecting surface is configured to have a shape of afree-form curved surface, it is possible to correct the curvature offield and the distortion aberration at a high accuracy.

Feature 10

In the projection optical system according to example embodiments of thepresent invention, in addition to Features 1 to 9, the image formingunit does not intersect the optical axis.

Since an axial light beam is not used, it is possible to control thecurvature of field and the distortion aberration at a high accuracy byusing the aspherical lens and the free-form curved mirror.

Feature 11

In the projection optical system according to example embodiments of thepresent invention, in addition to Features 1 to 10, at least the lenswhich is closest to the magnification side of the refraction opticalsystem is moved during focusing.

Accordingly, it is possible to control a curvature of field anddistortion which may occur due to focusing at a high accuracy. Morepreferably, floating focusing is used. Since a difference between theincidence angles of the light beams of the upper and lower ends of theimage plane to the screen are great, the variation in curvature of fieldis increased in the focusing according to the projection distance.Herein, since the floating focusing is used, it is possible to correctthe variation in curvature of field according to the variation in theprojection distance.

Feature 12

According to example embodiments of the present invention, there isprovided an image display apparatus including: an illumination opticalsystem which illuminates an image forming unit with light from a lightsource; and a projection optical system which projects an image formedin the image forming unit on a projection plane, in which the projectionoptical system is the projection optical system according to any one ofFeatures 1 to 11.

According to the feature, it is possible to obtain an image displayapparatus having a very small projection distance and a small size.

Specific Numerical Values of Examples

Next, Table 25 illustrated in FIG. 74 lists examples of numerical valuesassociated with the above-described conditions in the Examples 1 to 4.

Table 26 illustrated in FIG. 75 lists values according to each conditionin each Example.

As clarified from Tables 25 and 26, in the projection optical systemsaccording to Examples 1 to 4, the above-described values of theparameters associated with the conditions 1 to 5 are included within therange of each condition.

According the projection optical system specified by the above-describedspecific numerical examples, since an angle of a folded light beam, aneffective diameter of a lens, a distance between a folding mirror and alens, and a sag amount of an aspherical lens are set to appropriatevalues, it is possible to obtain a small-sized and high-performanceimage projection apparatus.

According to an embodiment of the present invention, it is possible toprovide a projection optical system having an extremely short projectiondistance and a small size.

In addition, although appropriate specific examples of the presentinvention are exemplified in the above-described embodiments, thepresent invention is not limited thereto.

In particular, specific shapes and numerical values of components inExamples 1 to 4 are merely exemplified for implementing the presentinvention, and thus, the scope of the prevention invention should not belimited thereto.

The present invention is not limited to the description of theembodiments, but appropriate changes and modifications can be madewithout departing from the spirit of the present invention.

What is claimed is:
 1. A projection optical system comprising: in orderfrom a reduction side to a magnification side, an image forming unitconfigured to form an image thereon; a refraction optical systemincluding a plurality of lenses; a first reflecting surface and a secondreflecting surface, wherein, when an optical axis shared by the largestnumber of lenses among optical lenses of the refraction optical systemis defined as an optical axis of the projection optical system; inarrangement where a distance between an intersection of amagnification-side surface of a lens which is arranged to be closest tothe magnification side of the refraction optical system and the opticalaxis and an intersection of the first reflecting surface and the opticalaxis has a minimum value, the distance between the intersections isdenoted by L, a focal length of the refraction optical system is denotedby f, a direction parallel to the optical axis is defined by a Z axisdirection, an arrangement direction of the first reflecting surface andthe second reflecting surface is defined by a Y axis direction, amaximum value of a distance between the optical axis and an end portionof the image forming unit in the Y axis direction is denoted by Ymax, ina YZ plane which is a plane parallel to the Y axis direction and the Zaxis direction, a maximum value D1 of a distance between an intersectionof a light beam path from the image forming unit and themagnification-side surface of the lens which is arranged to be closestto the magnification side of the refraction optical system and theoptical axis, a sag amount ds1 which is a sag amount of themagnification-side surface of the lens which is arranged to be closestto the magnification side of the refraction optical system at the D1 andof which positive direction is defined by the direction from thereduction side in the Z axis toward the magnification side, a point H ofwhich distance from the optical axis has a maximum value among theintersections of the light beam path and the first reflecting surface, apoint F of which distance from the optical axis has a minimum valueamong the intersections of the light beam path and the second reflectingsurface, an angle θ1 between a line connecting the H and the F and theoptical axis satisfies the condition 1: 0<Ymax/f−1/tan θ1; and condition2: −0.1<(L−D1−ds1)/(L+D1−ds1)−1/tan θ1.
 2. The projection optical systemaccording to claim 1, wherein, when an angle between a light beamemitted from the refraction optical system for an upper light beam atthe maximum angle of view in the Y axis direction and the optical axisis denoted by θ2, a distance between an intersection of the light beamemitted from the refraction optical system for the upper light beam atthe maximum angle of view in the Y axis direction and theclosest-magnification-side surface of the refraction optical system andthe optical axis is denoted by D2, and a sag amount which is a sagamount of the magnification-side surface of the lens which is arrangedto be closest to the magnification side of the refraction optical systemat a height of the D2 and of which positive direction is defined by thedirection from the reduction side in the Z axis toward the magnificationside is denoted by ds2, the angle θ2 satisfies the condition 3:0<Ymax/f−1/tan θ2; and condition 4: −0.05<(L−D2−ds2)/(L+D1−ds2)−1/tanθ2.
 3. The projection optical system according to claim 1, wherein thelens having a magnification-side surface and which is arranged to beclosest to the magnification side of the refraction optical system is anaspherical lens having a convex and aspherical surface.
 4. Theprojection optical system according to claim 3, wherein the lens havingthe magnification-side surface and which is the aspherical lens has anegative power on the optical axis and a positive power in theperiphery.
 5. The projection optical system according to claim 3,wherein the lens having the magnification-side surface and which is theaspherical lens is arranged between a spherical lens of which distancebetween an intersection of a lower light beam at the maximum angle ofview in the Y axis direction and a surface of the aspherical lens andthe optical axis is at maximum, and the first reflecting surface.
 6. Theprojection optical system according to claim 1, further comprising anaspherical lens having a negative power on the optical axis and apositive power in the periphery.
 7. The projection optical systemaccording to claim 6, wherein the aspherical lens is arranged between aspherical lens of which distance between an intersection of a lowerlight beam at the maximum angle of view in the Y axis direction and asurface of the aspherical lens and the optical axis is at maximum, andthe first reflecting surface.
 8. The projection optical system accordingto claim 1, wherein the first reflecting surface is a plane mirror andis rotated by 45 degrees on the YZ plane.
 9. The projection opticalsystem according to claim 1, wherein the second reflecting surface is aconcave mirror.
 10. The projection optical system according to claim 1,wherein in a focus state where the L is at minimum, when paraxialmagnification of the refraction optical system is denoted by β, thecondition 5: 5<β<8 is satisfied.
 11. The projection optical systemaccording to claim 1, wherein the second reflecting surface has a shapeof a free-form curved surface.
 12. The projection optical systemaccording to claim 1, wherein the image forming unit is prevented fromintersecting the optical axis.
 13. The projection optical systemaccording to claim 1, wherein at least the lens which is closest to themagnification side of the refraction optical system is moved duringfocusing.
 14. An image display apparatus comprising: an illuminationoptical system that illuminates the image forming unit with light from alight source; and a projection optical system that projects the imageformed on the image forming unit onto a projection plane, wherein theprojection optical system is the projection optical system according toclaim 1.